If they used Jewish dates on the years, they would create a pointless need to translate every date from one calendar to the other. The use of C.E. is a reasonable compromise which actually incorporates the Christian calendar as a base, changing the label but not the years.
That was my whole point though, why can't the Biblical Archaeology Review just use the Christian calendar A.D. instead of the politically correct C.E. It's a pet peeve that although the years are the same, so called academics have to deny Christianity and change the label.